Data types

1. Data types Outline • Primitive data types • Structured data types • Strings • Enumerated types • Arrays • Records • Pointers

2. Primitive data types Points • Numeric types • Booleans • Characters

3. Data types: introduction A data type is not just a set of objects. We must consider all operations on these objects. A complete definition of a type must include a list of operations, and their definitions.  Primitive data objects are close to hardware, and are represented directly (or almost directly) at the machine level—usually word, byte, bit.

4. Integer types An integer type is a finite approximation of the infinite set of integer numbers:{0, 1, -1, 2, -2, ...}. Various kinds of integers:signed—unsigned, long—short—small.  Hardware implementations of integers:one's complement, two's complement, ...

5. Floating-point types All "real" numbers in computers are finite approximations of the non-denumerable set of real numbers. Precision and range of values are defined by the language or by the programmer. Hardware implementations (used by floating-point processors): exponent and mantissa.

6. Boolean type This type is not supported by all languages (for example, it is not available in PL/, C, Perl). The values are true and false. Operations are as in classical two-valued propositional logic. Hardware implementation: a single bit or a byte (this allows more efficient operations).

7. Character types This is usually ASCII, but extended character (Unicode, ISO) sets are often used. Accented characters é à ü etc. should fit within ASCII, though there is no single standard. Chinese or Japanese are examples of writing systems that require character sets of many more than 256 elements. Hardware implementation: a byte (ASCII, EBCDIC), two bytes (Unicode) or several bytes.

8. Other primitive types • word (for example, in Modula-2) • byte, bit (for example, in PL/I) • pointer (for example, in C)

9. Structured data types Points • Strings • Enumerated types • Arrays • Records

10. Strings A string is a sequence of characters. It may be: • a special data type (its objects can be decomposed into characters)—Fortran, Basic; • an array of characters—Pascal, Ada; • a list of characters—Prolog; • consecutively stored characters—C. The syntax is the same: characters in quotes. Pascal has one kind of quotes, Ada has two: 'A' is a character, "A" is a string.

11. String operations Typical operations on strings string  string  string concatenation string  int  int  string substring string  characters decompose into an array or list characters  string convert an array or list into a string

12. String operations (2) string  integer length string  boolean is it empty? string  string  boolean equality, ordering

13. More string operations… Specialized string manipulation languages (Snobol, Icon) include built-in pattern matching, sometimes very complicated, with extremely elaborate backtracking. Another language that works very well with strings is, of course, Perl.

14. Fixed- and variable-length strings The allowed length of strings is a design issue: fixed-length strings—Pascal, Ada, Fortran; variable-length strings—C, Java, Perl. A character may be treated as a string of length 1, or as a separate data structure. Many languages (Pascal, Ada, C, Prolog) treat strings as special cases of arrays or lists. Operations on strings are the same as on arrays or lists of other types. For example, every character in a character array is available at once, whereas a list of characters must be searched linearly.

15. Enumerated types Also called: user-defined ordinal types[read Section 6.4] We can declare a list of symbolic constants that are to be treated literally, just like in Prolog or Scheme. We also specify the implicit ordering of those newly introduced symbolic constants. In Pascal: type day = (mo, tu, we, th, fr, sa, su); Here, we have mo < tu < we < th < fr < sa < su.

16. Operators for enumerated types Pascal supplies the programmer with three generic operations for every new enumerated type T: succ: successor, for example, succ(tu) = we pred: predecessor, for example, pred(su) = sa (each is undefined at one end) ord: (ordinal) position in the type, starting at 0,so for example ord(th) = 3 For characters, Pascal also has chr, producing the character at a given position, so for example chr(65) returns ‘A’.

17. Enumerated types in Ada Ada makes these generic operations complete: succ: successor, pred: predecessor, pos: position, val: constant at position. Ada also supplies type attributes, among them FIRST and LAST: day'FIRST = mo, day'LAST = su

18. Reuse of symbolic constants A design issue: is the symbolic constant allowed in more than one type? In Pascal, no. In Ada, yes: type stoplight is (red, amber, green); type rainbow is (violet, indigo, blue, green, yellow, orange, red); Qualified descriptions—similar to type casts—prevent any confusion: we can write stoplight'(red) or rainbow'(red).

19. Implementation of enumerated types Map the constants c1, ..., ck into small integers 0, ..., k-1. Enumerated types help increase clarity and readability of programs by separating concepts from their numeric codes.

20. Arrays An array represents a mapping: index_type  component_type The index type must be a discrete type (integer, character, enumeration etc). In some languages this type is specified implicitly: an array of size N is indexed 0…N-1 in C++ / Java / Perl, but in Fortran it is 1…N. In Algol, Pascal, Ada the lower and upper bound must be both given. There are normally few restrictions on the component type (in some languages we can even have arrays of procedures or files).

21. Multidimensional arrays Multidimensional arrays can be defined in two ways (for simplicity, we show only dimension 2): index_type1  index_type2  component_type This corresponds to references such as A[I,J]. Algol, Pascal, Ada work like this. index_type1 (index_type2  component_type) This corresponds to references such as A[I][J]. Java works like this. Perl sticks to one dimension

22. Operations on arrays (1) select an element (get or change its value): A[J] select a slice of an array: (read the textbook, Section 6.5.7) assign a complete array to a complete array: A := B; There is an implicit loop here.

23. Operations on arrays (2) Compute an expression with complete arrays (this is possible in extendible or specialized languages, for example in Ada): V := W + U; If V, W, U are arrays, this may denote array addition. All three arrays must be compatible (the same index and component type), and addition is probably carried out element by element.

24. Subscript binding static: fixed size, static allocation this is done in older Fortran. semistatic: fixed size, dynamic allocation Pascal. semidynamic: size determined at run time, dynamic allocation Ada dynamic: size fluctuates during execution, flexible allocation required Algol 68, APL—both little used...

25. Array-type constants and initialization Many languages allow initialization of arrays to be specified together with declarations: C int vector [] = {10,20,30}; Ada vector: array(0..2) of integer := (10,20,30); Array constants in Ada temp is array(mo..su)of -40..40; T: temp; T := (15,12,18,22,22,30,22); T := (mo=>15, we=>18, tu=>12, sa=>30, others=>22); T := (15,12,18, sa=>30, others=>22);

26. Implementing arrays (1) The only issue is how to store arrays and access their elements—operations on the component type decide how the elements are manipulated. An array is represented during execution by an array descriptor. It tells us about: the index type, the component type, the address of the array, that is, the data.

27. Implementing arrays (2) Specifically, we need: the lower and upper bound (for subscript checking), the base address of the array, the size of an element. We also need the subscript—it gives us the offset (from the base) in the memory area allocated to the array. A multi-dimensional array will be represented by a descriptor with more lower-upper bound pairs.

28. Implementing multidimensional arrays Row major order (second subscript increases faster) Column major order (first subscript increases faster)

29. Implementing multidimensional arrays (2) Suppose that we have this array: A: array [LOW1..HIGH1, LOW2..HIGH2] of ELT; where the size of each entity of type ELT is SIZE. This calculation is done for row-major (calculations for column-major are quite similar). We need the base—for example, the address LOC of A[LOW1, LOW2].

30. Implementing multidimensional arrays (3) We can calculate the address of A[I,J] in the row-major order, given the base. Let the length of each row in the array be: ROWLENGTH = HIGH2 - LOW2 + 1 The address of A[I,J] is: (I - LOW1) * ROWLENGTH * SIZE + (J - LOW2) * SIZE + LOC

31. Implementing multidimensional arrays (4) Here is an example. VEC: array [1..10, 5..24] of integer; The length of each row in the array is: ROWLENGTH = 24 - 5 + 1 = 20 Let the base address be 1000, and let the size of an integer be 4. The address of VEC[i,j] is: (i - 1) * 20 * 4 + (j - 5) * 4 + 1000 For example, VEC[7,16] is located in 4 bytes at 1524 = (7 - 1) * 20 * 4 + (16 - 5) * 4 + 1000

32. Languages without arrays A final word on arrays: they are not supported by standard Prolog and pure Scheme. An array can be simulated by a list, which is the basic data structure in Scheme and a very important data structure in Prolog. Assume that the index type is always 1..N. Treat a list of N elements: [x1, x2, ..., xN] (Prolog) (x1 x2 ... xN) (Scheme) as the (structured) value of an array

33. Records A record is a heterogeneous collection of fields (components)—this differs from homogenous arrays. Records are supported by a majority of important languages, beginning with Cobol, through Pascal, PL/I, Ada, C (where they are called structures), Prolog (!) to C++. There are no records in Java, but classes replace them. There are no records in Perl.

34. Ada records—syntax type date is record day: 1..31; month: 1..12; year: 1000..9999;end record;type person is record name: record fname: string(1..20); lname: string(1..20); end record; born: date; gender: (F, M);end record;

35. Fields A field is distinguished by a name rather than an index. Iteration on elements of an array is natural and very useful, but iteration on fields of a record is not possible (why?). A field is indicated by a qualified name. In Ada: X, Y: person; X.born.day := 15; X.born.month := 11; X.born.year := 1964; Y.born := (23, 9, 1949); Y.name.fname(1..8) := "Smithson";

36. Operations on records (1) Selection of a component is done by field name. Construction of a record from components—either from separate fields, or as a complete record in a structured constant. D := (month => 10, day => 15, year => 1994); D := (day => 15, month => 10, year => 1994); D := (15, 10, 1994); D := (15, 10, year => 1994); Note that an array can also be assigned such a constant. Interpretation depends on context. A: array(1..3)of integer; A := (15, 10, 1994);

37. Operations on records (2) Assignment of complete records is allowed in Ada, and is done field by field. Records can be compared for equality or inequality, regardless of their structure or type of components. No generic standard ordering of records exists, but specific ordering can be defined by the programmer.

38. More on records Ada allows default values for fields: type date is record day: 1..31; month: 1..12; year: 1000..9999 := 2002; end record; D: date; -- D.year is now 2002 There are almost no restrictions on field types. Any combination of records and arrays (any depth) is usually possible. A field could also be a file or even a procedure!

39. The Prolog equivalent of records Records—or rather terms—in Prolog can carry their type and their components around: date(day(15), month(10), year(1994)) person( name(fname("Jim"), lname("Berry")), born(date(day(15), month(10), year(1994))), gender(male) ) If we can assure correct use, this can be simplified by dropping one-argument "type" functors: date(15, 10, 1994) person(name("Jim", "Berry"), born(date(15, 10, 1994)), male)

40. Back to pointers [Note: We’re skipping 6.9.9] A pointer variable has addresses as values (and a special address nil or null for "no value"). They are used primarily to build structures with unpredictable shapes and sizes—lists, trees, graphs—from small fragments allocated dynamically at run time. A pointer to a procedure is possible, but normally we have pointers to data (simple and composite). An address, a value and usually a type of a data item together make up a variable. We call it an anonymous variable: no name is bound to it. Its value is accessed by dereferencing the pointer.

41. p   17 Back to pointers (2) Pointers in Pascal are quite well designed. Note that, as with normal named variables, in this: p^ := 23; we mean the address of p^ (the value of p). In this: m := p^; we mean the value of p^. value(p) =  value(p^) = 17

42. Pointer variable creation A pointer variable is declared explicitly and has the scope and lifetime as usual. An anonymous variable has no scope (because it has no name) and its lifetime is determined by the programmer. It is created (in a special memory area called heap) by the programmer, for example: new(p); in Pascal p = malloc(4); in C and destroyed by the programmer: dispose(p); in Pascal free(p); in C

43. Pointer variable creation (2) If an anonymous variable exists outside the scope of the explicit pointer variable, we have "garbage" (a lost object). If an anonymous variable has been destroyed inside the scope of the explicit pointer variable, we have a dangling reference. new(p); p^ := 23; dispose(p); ...... if p^ > 0 {???}

44. Pointer variable creation (2) Producing garbage, an example in Pascal: new(p); p^ := 23; new(p); {the anonymous variable with the value 23 becomes inaccessible} Garbage collection is the process of reclaiming inaccessible storage. It is usually complex and costly. It is essential in languages whose implementation relies on pointers: Lisp, Prolog.

45. Pointers: types and operators Pointers in PL/I are typeless. In Pascal, Ada, C they are declared as pointers to types, so that a dereferenced pointer (p^, *p) has a fixed type. Operations on pointers in C are quite rich: char b, c; c = '\007'; b = *((&c - 1) + 1); putchar(b);